The energy of a graph $ G $ is the sum of the absolute values of the eigenvalues of the
adjacency matrix of $ G $. Let $ s^+(G), s^-(G) $ denote the sum of the squares of the …

Let G be a regular graph with m edges, and let μ 1, μ 2 denote the two largest eigenvalues of
AG, the adjacency matrix of G. We show that, if G is not complete, then μ 1 2+ μ 2 2≤ 2 (ω …

In this short paper we prove that the sum of the squares of negative (or positive) eigenvalues
of the adjacency matrix of a graph is lower bounded by the sum of the degrees divided by …

Let $ G $ be a graph with $ n $ non-isolated vertices and $ m $ edges. The positive/negative
square energies of $ G $, denoted $ s^+(G) $/$ s^-(G) $, are defined as the sum of squares …

The Lov\'asz $\theta $-function, originally introduced as an upper bound on the Shannon
capacity of graphs, has many fascinating properties. The first part of this work relies on that …

This paper delves into three research directions, leveraging the Lovász ϑ-function of a
graph. First, it focuses on the Shannon capacity of graphs, providing new results that …

We prove the following local strengthening of Shearer's classic bound on the independence
number of triangle-free graphs: For every triangle-free graph $ G $ there exists a probability …

In this paper we prove a conjecture by Wocjan, Elphick and Anekstein (2018) which upper
bounds the sum of the squares of the positive (or negative) eigenvalues of the adjacency …

This paper delves into three research directions, leveraging the Lovász $\vartheta $-function
of a graph. First, it focuses on the Shannon capacity of graphs, providing new results that …

Bollobás and Nikiforov [2] proposed a conjecture that for any non-complete graph G with m
edges and clique number ω, the following inequality holds: λ 1 2+ λ 2 2≤ 2 (1− 1 ω) m …